Generalized Sequential Differential Calculus for Expected-Integral Functionals

TL;DR

This paper develops a generalized calculus framework for expected-integral functionals, enabling the derivation of sequential Leibniz rules for subgradients, which is useful in stochastic programming applications.

Contribution

It introduces and studies expected-integral functionals and establishes sequential Leibniz rules for regular subgradients using variational analysis techniques.

Findings

Established sequential Leibniz rules for expected-integral functionals.

Developed new variational analysis tools for stochastic programming.

Enhanced understanding of subdifferential calculus in integral functional settings.

Abstract

Motivated by applications to stochastic programming, we introduce and study the expected-integral functionals, which are mappings given in an integral form depending on two variables, the first a finite dimensional decision vector and the second one an integrable function. The main goal of this paper is to establish sequential versions of Leibniz's rule for regular subgradients by employing and developing appropriate tools of variational analysis.